The relative pair-production rates by 1.064- and 1.770-MeV photons on Ge were measured in a double-escape-peak pair spectrometer consisting of a 2.44-cm diameter by 1-cm-thick intrinsic, planar Ge detector inside of a split NaI(Tl) annulus. Guided by previous experiments, the theoretical cross section $\sigma \mathrm{}\left(1.770\right)\mathrm{}$ was assumed to be correct and the value $\sigma \mathrm{}\left(1.064\right)=0.131\mathrm{}\pm 0.012$ mb/atom was deduced from the data. This is in excellent agreement with recent direct numerical screened calculations of Tseng and Pratt.

We have employed the eikonal method to calculate the cross section for the capture of an electron into an arbitrary $\mathrm{nl}$ subshell in collisions between hydrogen atoms and fast projectiles. The projectiles were protons, ${\mathrm{C}}^{6+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{Fe}}^{24+}$. The energy ranges considered were 20-100 keV in the proton case and 40-200 keV per nucleon in the other cases. These projectiles were selected because of their importance in fusion plasmas. For the highly charged case of ${\mathrm{Fe}}^{24+}$ we found that our formulas, while exact, involved a high degree of cancellation and produced unreliable numerical results, so that a numerical integration of the penultimate formula was substituted. In the proton case, agreement with recent experimental data is excellent.

The eikonal approach developed previously for calculating electron-capture cross sections for bare projectiles colliding with hydrogenic targets is extended here to allow for multielectron targets. Both the impact and wave pictures are employed and their equivalence is discussed. As a first approximation, each atomic orbital is specified by the three hydrogenic quantum numbers, an effective nuclear charge $Z_t$, and an energy eigen-value in the impact picture, or ionization potential in the wave picture. The $Z_t^{\prime }$ appearing in the eikonal phase factor is left undetermined because of incomplete information on the many-body target. However, analytic expressions are derived for the theoretical cross sections, and numerical values are calculated for simple choices of $Z_t^{\prime }$. Those results are compared with existing experimental data for C, Ne, Ar, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and He targets.

Electron-impact excitation cross sections of the $a{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state of the ${\mathrm{N}}_2$ molecule are calculated by the method of close coupling with full allowance for electron exchange for incident-electron energies of 12.5-50 eV. The wave functions of the two states involved are calculated by the self-consistent-field method with ten $s$-type and six $p$-type Gaussian orbitals as basis functions. The present calculation agrees very well with experiments above 30 eV, but a substantial difference is found below 30 eV.

A secondary-ion recoil source was used to study charge transfer and ionization in collisions of ${\mathrm{Ar}}^{q+} \left(2\mathrm{}\le q\le 9\right)$ on Ne at projectile energies between 100 and 1100 eV per projectile charge. Two experimental methods are presented. With the first one we measure cross sections for electron capture by detecting both the initial and final charge states of the Ar ions. With the second method we measure, in addition to those parameters, the charge state of the Ne ions after the reaction. This three-parameter method allows us to distinguish among various competing reaction mechanisms and to measure cross sections for single- and multiple-electron capture, ionization, and transfer ionization. We find that the cross sections for ionization without simultaneous capture are negligibly small, whereas those for transfer ionization are quite important in several cases.

A general procedure is proposed to treat a many-state atomic-collision problem involving both nonadiabatic radial and rotational couplings. The procedure is based on the classical $S$-matrix theory in a new "dynamical-state" representation. The dynamical states are defined as the eigenstates of a new Hamiltonian operator which is composed of an ordinary electronic Hamiltonian and a Coriolis coupling term. The dynamical potential energies thus obtained avoid crossings even for the rotationally coupled states. At these avoided crossing points the rotationally induced transitions predominantly occur, which are delocalized in the ordinary adiabatic-state representation. The theory is applied to certain two-state- and three-state-model problems, and is shown to work well. An interesting catalytic phenomenon is found in a three-state problem. A certain transition is enhanced by a rotational coupling not directly associated with that transition; besides, a transition directly induced by that rotational coupling is not affected by the coupling responsible for the first transition. This phenomenon can be successfully explained and reproduced by the theory. A condition is discussed for this kind of phenomenon to occur in a general many-state collision problem involving rotational couplings.

Exact asymptotic wave functions are included in the basis set for variational calculations of the $K$ matrix in a multichannel model problem. Rapid convergence to exact results is demonstrated for both the variational $R$-matrix method and for the restricted-interpolated-anomaly-free (RIAF) variant of the Hulthén-Kohn method. If "irregular" asymptotic functions are omitted, convergence of the $R$-matrix calculations is much less satisfactory. By a particular choice of the form of discrete basis functions, vanishing at a fixed radius $r_1$ in the model problem, the main computational steps of both methods are made to be identical.

Scaled intermediate-coupling electron-impact collision strengths $Z^2\Omega$ and electric-dipole line strengths $Z^{2}S$ together with transition energies are calculated for selected transitions between the lower group of mixed states $2s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, $2p^2{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, and $2p^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and the upper group of mixed states $2s3p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2s3p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2p3s{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2p3s{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2p3d{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$, $2p3d{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, and $2p3d{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ in Be-like ions with nuclear charge number $Z$ in the range $14\le Z\le 54$. The results for $Z^2\Omega$ are given for eight impact electron energies in the range $1\le \epsilon \le 10$, where $\epsilon$ is the impact electron energy in threshold units. The results for transition energies and oscillator strengths are in good agreement with the experimental energies and with the energies and oscillator strengths for ${\mathrm{V}}^{19+}$, ${\mathrm{Fe}}^{22+}$, and ${\mathrm{Ni}}^{24+}$ calculated with Cowan's programs.

The theory of electron-atom scattering in the presence of a static external field, consisting of crossed electric and magnetic components, is formulated here and an approximate expression for the transition amplitude is obtained. The approximation involves as input the on-shell amplitude for scattering in the absence of the field; the field has the effect of modifying the electron momenta before and after the scattering in precisely the way which would be predicted assuming the electron to follow a classical trajectory in the field with the collision taking place instantaneously. If one attempts to derive this result by taking the zero-frequency limit of the amplitude for scattering in a plane-wave laser field, one obtains infinite values for the classical momenta. To avoid this difficulty—an infrared divergence of sorts—a more realistic model of the scattering process, in which the electron spends only a finite amount of time in the field, must be invoked. One such model, involving a laser pulse of sufficiently simple form to allow for the construction of wave packets whose motion through the field can be traced explicitly, is adopted here. The static-field results are obtained as the zero-frequency limit, which is well defined in this model.

Self-consistent-field and configuration-interaction potentials proposed for the ${\mathrm{H}}^{-}$ + He, ${\mathrm{Br}}^{-}$ + He, and ${\mathrm{Cl}}^{-}$ + Ar systems are tested by comparing measured values of the mobility and diffusion coefficients describing ion motion in gases with those calculated from the potentials and the two- and three-temperature kinetic theories. Tests are also made of the ion-atom potentials derived for these systems from scattering measurements with ion beams.

In this work we represent the static potential of an electron interacting with an atom by a sum of two Debye-Hückel or Yukawa functions. We approximate the nonlocal exchange term by an attractive, velocity-dependent potential using the effective-mass approximation with a regularized Yukawa form factor. This is transformed to an approximate local but energy-dependent potential. We also include an imaginary term with a regularized Yukawa form factor in the static potential. We apply this framework to a description of the bound and scattering states of electrons interacting with atomic oxygen and electrons interacting with neon. The results suggest that a small degree of velocity or energy dependence yields improvements with respect to the use of strictly static electron-atom potentials. In applications to atomic physics the formalism which is economical in parameters should serve as a simple parametrization of experimental data and as a means of extrapolation and interpolation of experimental observations.

We have computed direct and charge-exchange excitation cross sections for (a) ${\mathrm{He}}^{2+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions at projectile energies 1 - 20 keV, and for (b) ${\mathrm{H}}^{+}-{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ collisions at c.m. energies 1.6 to 8 keV, using the close-coupling method with He${\mathrm{H}}^{2+}$ molecular states as basis and electron translation-factor corrections based on molecular-state switching functions. Basis sets with up to 10 and 12 molecular states have been used, and good convergence of results as a function of basis size is found. The results are compared with recent theoretical calculations of Winter, Lane, and Hatton and with experimental values. For process (a) total charge-transfer cross sections are in generally good agreement with those found by Winter et al. using Bates-McCarroll translation factors and, less quantitatively, so are individual state cross sections for ${\mathrm{He}}^{+}(2s,2\mathrm{}{p}_0,2\mathrm{}{p}_{\pm 1}$). For process (b) significant differences with the results of Winter et al. are found; these appear to be traceable to the different treatments of the electron translational factors used. Charge-transfer cross sections of Winter, Hatton, and Lane [Phys. Rev. A 22, 930 (1980)] are 14 - 32% higher than those found here using comparable basis sets, and individual state cross sections for direct excitation to ${\mathrm{He}}^{+}(2s,2\mathrm{}{p}_0,2\mathrm{}{p}_{\pm 1}$) are also systematically larger than ours (by as much as a factor of 2 in some cases), although values for individual states are only poorly converged in both calculations. Very good agreement is found in all cases with recent experimental measurements.

Elastic and rotationally inelastic differential cross sections are calculated for slow neutrons incident on gaseous para-$\mathrm{H}_2^{}{}_{}{}^{+}$. This target is chosen as the simplest open-shell molecular system so that the contribution of electromagnetic forces to the scattering can be studied. It is shown that electromagnetic forces are dominant over nuclear forces in $0\to 2$ rotational excitation for small-momentum-transfer collisions (low angles at incident energies about twice the $0\to 2$ threshold value). For large-momentum-transfer collisions (wide angles at the higher energies or all angles at energies close to threshold) nuclear forces dominate the scattering. The calculations show that low-angle, small-energy-loss experiments would isolate the weak but long-range electromagnetic forces and thus probe target electronic structure.

A formal, iterative perturbation series is developed for the inverse of the scattering length, in powers of the coupling constant $\lambda$. An analysis of the series is carried out for two examples of screened Coulomb potentials. It allows us to isolate the nearby singularities and hence obtain the analytic continuations for the scattering length, which are valid over a large range of values of $\lambda$.

Charge-transfer cross sections from the ground state of atomic hydrogen into the final $1s$, $2s$, $2p$, $3s$, $3p$, and $3d$ excited states of the ${\mathrm{Li}}^{2+}$ ion by the impact of fully stripped lithium ions are calculated in the Coulomb-Born and Born approximations. The results for the total charge-transfer cross sections are compared with the existing experimental findings and other theoretical calculations. The present calculated results obtained by the Coulomb-Born approximation are found to be in excellent agreement with the experimental results throughout the energy region considered, except in the low-energy region $E<\mathrm{}275\mathrm{}$ keV, whereas the present Born results grossly overestimate the experimental findings. The existing theoretical results obtained for the unitarized-distorted-wave approximation or obtained by the Monte Carlo approach are in better agreement with the observed values in the low-energy region, as compared with the present Coulomb-Born or Born results. However, with an increase of the incident-ion energy, the earlier calculated results show poor agreement with the observed values.

One-photon free-free absorption amplitudes are derived for electrons scattering from a spinless spherically symmetric target in the dipole approximation. The exact amplitudes are compared to the usual on-shell approximation to the amplitudes. An effect analogous to the Fano effect in bound-free transitions is also found in free-free transitions if off-shell terms are retained in the amplitudes. Methods of detecting the off-shell effects experimentally are discussed.

The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.

It is shown that a suitably large magnetic field oriented at the "magic angle" $invcos\left(\frac{1}{\sqrt{3}}\right)\simeq 54.7^{\circ }$ with respect to the electric vector of linearly polarized light eliminates the photoexcitation transition-rate inhomogeneity which normally causes atoms initially in different Zeeman states to be excited at different rates. The equations describing single-photon and resonant multiphonon photoionization via an autoionizing state then reduce to simple rate equations for the populations in various energy levels; their Zeeman states remain equally populated throughout and need not be followed individually. For a given light fluence, the photoion yield is optimized when the inhomogeneity disappears. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding bound-bound atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogenous linewidths.

Analytic expressions are obtained for relativistic radiative-decay rates of transitions between the $L$ and $K$ shells of intermediate- and high-$Z$ elements. These single-electron transition rates in a central potential can be expressed as a power series in the atomic scale parameter $\lambda$ which characterizes a small-distance expansion of the relativistic screened atomic potential. Retardation effects and all multipole contributions of the radiation field are included. With this approach it is possible to trace explicitly, both for the point Coulomb potential and for screening modifications, the role of relativistic, retardation, and higher multipole contributions in modifying the corresponding nonrelativistic dipole transition rates.

The implicit summation technique used to calculate the $N-1\mathrm{}$ sums over the intermediate states appearing in the expression of the $N$-photon transition amplitude provided by the lowest-order perturbation theory is generalized to the calculation of the transition amplitude resulting from the resummation of the whole perturbation series. The method is illustrated by two-photon ionization.